Properties

Label 4.5
Level 4
Weight 5
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(4))\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 4q^{2} + 16q^{4} - 14q^{5} - 64q^{8} + 81q^{9} + O(q^{10}) \) \( q - 4q^{2} + 16q^{4} - 14q^{5} - 64q^{8} + 81q^{9} + 56q^{10} - 238q^{13} + 256q^{16} + 322q^{17} - 324q^{18} - 224q^{20} - 429q^{25} + 952q^{26} + 82q^{29} - 1024q^{32} - 1288q^{34} + 1296q^{36} + 2162q^{37} + 896q^{40} - 3038q^{41} - 1134q^{45} + 2401q^{49} + 1716q^{50} - 3808q^{52} + 2482q^{53} - 328q^{58} - 6958q^{61} + 4096q^{64} + 3332q^{65} + 5152q^{68} - 5184q^{72} + 1442q^{73} - 8648q^{74} - 3584q^{80} + 6561q^{81} + 12152q^{82} - 4508q^{85} - 9758q^{89} + 4536q^{90} - 1918q^{97} - 9604q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4.5.b \(\chi_{4}(3, \cdot)\) 4.5.b.a 1 1